LAS VEGAS — The Andrea Bargnani Era begins Wednesday with the Knicks, and the J.R. Smith Era formally rages on at least three more years at the Garden.

The Bargnani trade and Smith’s four-year, $24.7 million deal will finally be announced Wednesday, when the NBA’s free-agency signing period begins.

The Knicks gave Smith the maximum amount allowable under the Early-Bird-Rights rules, which pertains to players who have been on the team for just two seasons. They were fairly lucky no team made an offer that blew Smith out of the water, according to his brother, Chris Smith.

“He’s better than a lot of guys who got bigger checks than him,’’ Chris Smith said at the Knicks’ first summer-league practice. “He’s a humble guy. He’ll keep working and we’ll see next time free agency comes around.’’

Chris Smith will be the Knicks summer-league team’s starting point guard after rehabbing from a knee patella tear suffered last training camp. J.R. Smith will come here this week to watch the first two games.

J.R. Smith has an opt-out after the third year. His market value took a hit after a poor postseason.

“His mood is great,’’ Chris Smith said of his brother. “He’s ready and willing and going to make his best run at a championship. Hopefully the Knicks come out on top and I’m a part of it.

“My goal is to get to training camp, make the team and have the brotherly tandem everyone’s talking about.’’

The cap-strapped Knicks are struggling to sign free agents from other teams and yesterday learned from agent David Falk they are no longer in the running for power forward Elton Brand. An NBA source said Brand’s market has risen higher than the Knicks can offer — the story of their summer.

Unless Metta World Peace decides not to retire, the Bargnani/Smith acquisitions will serve as the Knicks’ biggest splashes. The 7-foot sweet-shooting Italian didn’t live up to the enormous hype as the No. 1 overall pick in Toronto, but the Knicks believe he will thrive in the Big Apple without the grandiose expectations.

The Knicks haven’t been able to comment about Bargnani. According to a person familiar with their thinking, the franchise views Bargnani’s game sinking in Toronto his final three years as being related to Chris Bosh departing for the Heat.

Forced to be the biggest name on the club and the top scoring option, Bargnani wilted after enjoying his best days as second fiddle to Bosh.

With the Knicks, Bargnani will be at best a second option, maybe less. Carmelo Anthony has J.R. Smith, his wingman last season, and point guard Raymond Felton. Not that the Knicks don’t have big plans for Bargnani.

Bargnani might not start, but they envision him finishing games as a primary option down the stretch, especially when Smith is floundering. The Knicks also feel Bargnani’s presence will allow their offense to run at a faster tempo. They love his range and feel he can score in the low post.

“He’s a skilled big who can score around the basket and it will take weight off Tyson [Chandler],’’ Chris Smith said.

The Knicks were desperate for another big man who can score alongside Chandler. That’s because there are plans to put Amar’e Stoudemire on restrictions next season — possibly at 20 minutes a night and a major limit on him playing in back-to-backs.

The trade couldn’t become official until today due to Quentin Richardson’s sign-and-trade inclusion. Former longtime Olympia Milano head coach Dan Peterson said he thinks the Knicks hit the jackpot with Bargnani.

“I think the move to the Knicks is ideal for Andrea,’’ Peterson, who coached Mike D’Antoni in Italy said. “He’s been in Toronto for seven years and there are times when a player needs a fresh start.“I’ve always felt he was hurt by being the No. 1 pick in that one year [2006] when the high-school players all had to go one year to the NCAA. If [Greg] Oden and [Kevin] Durant and others would have been in that draft, Bargnani would not have gone No. 1 and would not have been weighed down by expectations.

“The Knicks won’t have to deal with that. They didn’t get him because he was No. 1. They got him because they think he can help them. Period.’’

Bargnani is in New York meeting with Knicks brass. He’s slated to play for the Italian National Team in the European Championships that begin Sept. 4.